Optimum Wordlength Search Using Sensitivity Information
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Optimum Wordlength Search Using Sensitivity Information Kyungtae Han and Brian L. Evans Embedded Signal Processing Laboratory, Wireless Networking and Communications Group, The University of Texas at Austin, Austin, TX 78712, USA Received 2 October 2004; Revised 4 July 2005; Accepted 12 July 2005 Many digital signal processing algorithms are first developed in floating point and later converted into fixed point for digital hardware implementation. During this conversion, more than 50% of the design time may be spent for complex designs, and optimum wordlengths are searched by trading off hardware complexity for arithmetic precision at system outputs. We propose a fast algorithm for searching for an optimum wordlength. This algorithm uses sensitivity information of hardware complexity and system output error with respect to the signal wordlengths, while other approaches use only one of the two sensitivities. This paper presents various optimization methods, and compares sensitivity search methods. Wordlength design case studies for a wireless demodulator show that the proposed method can find an optimum solution in one fourth of the time that the local search method takes. In addition, the optimum wordlength searched by the proposed method yields 30% lower hardware implementation costs than the sequential search method in wireless demodulators. Case studies demonstrate the proposed method is robust for searching for the optimum wordlength in a nonconvex space. Copyright © 2006 K. Han and B. L. Evans. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Digital signal processing algorithms often rely on long wordlengths for high precision, whereas digital hardware implementations of these algorithms need short wordlengths to reduce total hardware costs. Determining the optimum wordlength can be time-consuming if assignments of wordlengths are performed by trial and error. In a complex system, 50% of the design time may be spent on wordlength determination [1]. Optimum wordlength choices can be made by solving equations when propagated quantized errors [2] are expressed in an analytical form. However, an analytical form is difficult to obtain in complicated systems. Searching the entire space by simulation guarantees to find optimum wordlength. Computation time, however, increases exponentially as the number of wordlength variables increases. For these reasons, many simulation-based wordlength optimization methods have explored a subset of the entire space [3–7]. Choi and Burleson [3] showed how a general searchbased wordlength optimization can produce optimal or near-optimal solutions for different objective-constraint formulations. Sung and Kum [4] proposed simulation-based
wordlength optimization for fixed-point digital signal processing systems. These search algorithms try to find the cost-optimal solution by using either “exhaustive” search
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